Assignment problem with conflicts

Temel Öncan (Corresponding author), Zeynep Şuvak, Hakan Akyuz, I. Kuban Altinel

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)


We focus on an extension of the assignment problem with additional conflict (pair) constraints in conjunction with the assignment constraints and binary restrictions. Given a bipartite graph with a cost associated with each edge and a conflict set of edge pairs, the assignment problem with conflict constraints corresponds to finding a minimum weight perfect matching without any conflicting edge pair. For example, some chemicals cannot be processed on close processors, food and toxic products cannot be stored neighboring locations at the same storage area, and machines cannot be sent to process jobs without satisfying some spatial constraints. Unlike the well-known assignment problem, this problem is NP-hard. We first introduce a realistic special class and demonstrate its polynomial solvability. Then, we propose a Branch-and-Bound algorithm and a Russian Doll Search algorithm using the assignment problem relaxations for lower bound computations, and introduce combinatorial branching rules based on the conflicting edges in an optimal solution of the relaxations. According to the extensive computational experiments we can say that the proposed algorithms are very efficient.

Original languageEnglish
Pages (from-to)214-229
Number of pages16
JournalComputers & Operations Research
Publication statusPublished - Nov 2019
Externally publishedYes


  • Assignment Problem
  • Integer programming
  • Branch and bound
  • Conflicts
  • Branch-and-bound
  • Assignment problem


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